hmatrix-glpk-0.4.0: Linear Programming based on GLPK

Numeric.LinearProgramming

Description

This module provides an interface to the standard simplex algorithm.

For example, the following LP problem

maximize 4 x_1 - 3 x_2 + 2 x_3 subject to

2 x_1 + x_2 <= 10 x_3 + 5 x_4 <= 20

and

x_i >= 0

can be solved as follows:

```import Numeric.LinearProgramming

prob = Maximize [4, -3, 2]

constr1 = Sparse [ [2#1, 1#2] :<=: 10
, [1#2, 5#3] :<=: 20
]
```
````>>> ````simplex prob constr1 []
```Optimal (28.0,[5.0,0.0,4.0])
```

The coefficients of the constraint matrix can also be given in dense format:

```constr2 = Dense [ [2,1,0] :<=: 10
, [0,1,5] :<=: 20
]
```

By default all variables are bounded as `x_i >= 0`, but this can be changed:

````>>> ````simplex prob constr2 [ 2 :>=: 1, 3 :&: (2,7)]
```Optimal (22.6,[4.5,1.0,3.8])
```
````>>> ````simplex prob constr2 [Free 2]
```Unbounded
```

The given bound for a variable completely replaces the default, so `0 <= x_i <= b` must be explicitly given as `i :&: (0,b)`. Multiple bounds for a variable are not allowed, instead of `[i :>=: a, i:<=: b]` use `i :&: (a,b)`.

Synopsis

# Documentation

Constructors

 Maximize [Double] Minimize [Double]

Constructors

 Dense [Bound [Double]] Sparse [Bound [(Double, Int)]]

data Bound x Source

Constructors

 x :<=: Double x :>=: Double x :&: (Double, Double) x :==: Double Free x

Instances

 Show x => Show (Bound x)

(#) :: Double -> Int -> (Double, Int) infixl 5 Source

Coefficient of a variable for a sparse representation of constraints.

data Solution Source

Constructors

 Undefined Feasible (Double, [Double]) Infeasible (Double, [Double]) NoFeasible Optimal (Double, [Double]) Unbounded

Instances

 Show Solution